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      2019年6月1日 下午
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              <p>假设要用<code>JavaScript</code>实现一个阶乘函数，很容易想到用递归实现:<br><pre><code class="hljs javascript"><span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">factorial</span>(<span class="hljs-params">n</span>) </span>&#123;
  <span class="hljs-keyword">if</span>(n === <span class="hljs-number">1</span>) &#123;
    <span class="hljs-keyword">return</span> <span class="hljs-number">1</span>
  &#125;
  <span class="hljs-keyword">return</span> n * factorial(n<span class="hljs-number">-1</span>)
&#125;

<span class="hljs-built_in">console</span>.log(factorial(<span class="hljs-number">4</span>))   <span class="hljs-comment">// 24</span></code></pre></p>
<p>在上述代码中，由于最后一步返回了一个表达式(<code>n * factorial(n-1)</code>)，所以会保留<code>n</code>这个变量和函数<code>factorial(n-1)</code>的调用位置等信息，从而形成一层层的调用帧。</p>
<p>递归十分消耗内存，因为要同时保存非常多个调用记录，容易出现”栈溢出”错误<code>(Stack Overflow)</code></p>
<a id="more"></a>
<h1 id="尾调用"><a href="#尾调用" class="headerlink" title="尾调用"></a>尾调用</h1><p>尾调用是指的一个函数的最后一个动作是返回另一个函数的调用<br><pre><code class="hljs javascript"><span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">foo</span>(<span class="hljs-params">n</span>) </span>&#123;
  <span class="hljs-keyword">return</span> meh(n)
&#125;

<span class="hljs-comment">// 并不一定要在函数尾部，只要是最后一步操作即可</span>
<span class="hljs-comment">// 以下meh 和nco 函数均属于尾调用</span>
<span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">foo</span>(<span class="hljs-params">n</span>) </span>&#123;
  <span class="hljs-keyword">if</span>(n&gt;<span class="hljs-number">0</span>) &#123;
    <span class="hljs-keyword">return</span> meh(n)
  &#125;
  <span class="hljs-keyword">return</span> nco(n)
&#125;</code></pre></p>
<!-- moer -->
<p>不属于尾调用的情况<br><pre><code class="hljs javascript"><span class="hljs-comment">// 函数调用后还有赋值操作，所以不属于尾调用，即使语义一样</span>
<span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">foo</span>(<span class="hljs-params">n</span>) </span>&#123;
  <span class="hljs-keyword">let</span> tmp = meh(n)
  <span class="hljs-keyword">return</span> tmp
&#125;

<span class="hljs-comment">// 函数调用后还有相加操作</span>
<span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">foo</span>(<span class="hljs-params">n</span>) </span>&#123;
  <span class="hljs-keyword">return</span> meh(n) + <span class="hljs-number">1</span>
&#125;

<span class="hljs-comment">// 没有返回函数调用</span>
<span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">foo</span>(<span class="hljs-params">n</span>) </span>&#123;
  meh(n)
&#125;</code></pre></p>
<h1 id="尾调用优化"><a href="#尾调用优化" class="headerlink" title="尾调用优化"></a>尾调用优化</h1><blockquote>
<p>　　函数调用会在内存形成一个”调用记录”，又称”调用帧” (call frame)，保存调用位置和内部变量等信息。如果在函数A的内部调用函数B，那么在A的调用帧上方，还会形成一个B的调用帧。等到B运行结束，将结果返回到A，B的调用帧才会消失。如果函数B内部还调用函数C，那就还有一个C的调用帧，以此类推。所有的调用帧，就形成一个”调用栈” (call stack)。<br>　　尾调用由于是函数的最后一步操作，所以不需要保留外层函数的调用帧，因为调用位置、内部变量等信息都不会再用到了，只要直接用内层函数的调用帧，取代外层函数的调用帧就可以了。</p>
</blockquote>
<p>举例:<br><pre><code class="hljs javascript"><span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">getItem</span>(<span class="hljs-params">item</span>) </span>&#123;
  <span class="hljs-keyword">return</span> item
&#125;

<span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">foo</span>(<span class="hljs-params"></span>) </span>&#123;
  <span class="hljs-keyword">let</span> a=<span class="hljs-number">1</span>
  <span class="hljs-keyword">let</span> b=<span class="hljs-number">2</span>
  <span class="hljs-keyword">return</span> getItem(a+b)
&#125;
foo()</code></pre></p>
<p>上述代码中，如果函数<code>getItem</code>不是尾调用，函数<code>foo</code>就要保存内部变量<code>m</code>和<code>n</code>的值，以及函数<code>getItem</code>的调用位置等信息。<br>但如果调用<code>getItem</code>后，函数<code>foo</code>就结束了，所以执行到最后一步，可以删除<code>foo</code>的调用帧，只保留<code>getItem(3)</code>的调用帧。</p>
<blockquote>
<p>“尾调用优化” (Tail call optimization)，即只保留内层函数的调用帧。<br><strong>PS: 只有不再用到外层函数的内部变量，内层函数的调用帧才会取代外层函数的调用帧，否则就无法进行”尾调用优化”。</strong></p>
</blockquote>
<h1 id="尾递归"><a href="#尾递归" class="headerlink" title="尾递归"></a>尾递归</h1><p>函数调用自身，称为递归；如果尾调用自身，就称为尾递归。</p>
<blockquote>
<p>对于尾递归来说，由于只存在一个调用帧，所以能有效的避免”栈溢出”错误的发生。</p>
</blockquote>
<!-- <s>"尾调用优化"对递归操作意义重大，所以ES6也明确规定了，所有`ECMAScript`的实现，都必须部署"尾调用优化"。</s> -->
<p>改写之前的代码:<br><pre><code class="hljs javascript"><span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">factorial</span>(<span class="hljs-params">n,total</span>) </span>&#123;
  <span class="hljs-string">"use strict"</span>
  total = total || <span class="hljs-number">1</span>
  <span class="hljs-keyword">if</span>(n &lt;= <span class="hljs-number">1</span>) <span class="hljs-keyword">return</span> total
  <span class="hljs-keyword">return</span> factorial(n<span class="hljs-number">-1</span>, n*total)
&#125;</code></pre></p>
<p><strong>ES6的尾调用优化只在严格模式下开启，正常模式是无效的</strong></p>
<p>在正常模式下，函数内部有两个变量，可以跟踪函数的调用栈。</p>
<ul>
<li>arguments: 返回调用时函数的参数。</li>
<li>caller: 返回调用当前函数的那个函数。</li>
</ul>
<p>尾调用优化发生时，函数的调用栈会改写，因此上面两个变量就会失真。严格模式禁用这两个变量，所以尾调用模式仅在严格模式下生效。</p>
<p>参考:  </p>
<blockquote>
<p><a href="https://github.com/tc39/proposal-ptc-syntax/blob/master/README.md" target="_blank" rel="noopener">https://github.com/tc39/proposal-ptc-syntax/blob/master/README.md</a></p>
</blockquote>
<p><strong>补充(2019.06.02): 出于某些因素的考虑，目前V8引擎中的尾递归优化已经被去掉了</strong></p>
<p>大概原因可以看这篇博客:  </p>
<blockquote>
<p><a href="https://imweb.io/topic/5a244260a192c3b460fce275" target="_blank" rel="noopener">https://imweb.io/topic/5a244260a192c3b460fce275</a></p>
</blockquote>
<h1 id="尾递归优化的实现"><a href="#尾递归优化的实现" class="headerlink" title="尾递归优化的实现"></a>尾递归优化的实现</h1><p>正常模式下如何实现尾递归优化呢?</p>
<pre><code class="hljs javascript"><span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">sum</span>(<span class="hljs-params">x,y</span>) </span>&#123;
  <span class="hljs-keyword">if</span> (y &gt; <span class="hljs-number">0</span>) &#123;
    <span class="hljs-keyword">return</span> sum(x + <span class="hljs-number">1</span>, y - <span class="hljs-number">1</span>);
  &#125; <span class="hljs-keyword">else</span> &#123;
    <span class="hljs-keyword">return</span> x;
  &#125;
&#125;
sum(<span class="hljs-number">1</span>,<span class="hljs-number">100000</span>)</code></pre>
<p>尾递归之所以需要优化，原因是调用栈太多，造成溢出，那么只要减少调用栈，就不会溢出。</p>
<pre><code class="hljs javascript"><span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">tco</span>(<span class="hljs-params">f</span>) </span>&#123;
  <span class="hljs-keyword">var</span> value;
  <span class="hljs-keyword">var</span> active = <span class="hljs-literal">false</span>;
  <span class="hljs-keyword">var</span> accumulated = [];

  <span class="hljs-keyword">return</span> <span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">accumulator</span>(<span class="hljs-params"></span>) </span>&#123;
    accumulated.push(<span class="hljs-built_in">arguments</span>);
    <span class="hljs-keyword">if</span> (!active) &#123;
      active = <span class="hljs-literal">true</span>;
      <span class="hljs-keyword">while</span> (accumulated.length) &#123;
        value = f.apply(<span class="hljs-keyword">this</span>, accumulated.shift());
      &#125;
      active = <span class="hljs-literal">false</span>;
      <span class="hljs-keyword">return</span> value;
    &#125;
  &#125;;
&#125;

<span class="hljs-keyword">var</span> sum = tco(<span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">sum</span>(<span class="hljs-params">x,y</span>) </span>&#123;
  <span class="hljs-keyword">if</span> (y &gt; <span class="hljs-number">0</span>) &#123;
    <span class="hljs-keyword">return</span> sum(x + <span class="hljs-number">1</span>, y - <span class="hljs-number">1</span>);
  &#125; <span class="hljs-keyword">else</span> &#123;
    <span class="hljs-keyword">return</span> x;
  &#125;
&#125;)

sum(<span class="hljs-number">1</span>,<span class="hljs-number">100000</span>)</code></pre>
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